It depends on how many Accordance modules you own and what other apps you plan on downloading. As far as Accordance is concerned, my guess is you'll probably be fine with 16 GB unless you own a lot of modules that include hi-res images.

Darin is correct,
my strong suggestion is that you should get a bigger iPhone if you can possibly afford it. Music/soundfiles can take up a huge amount of space, as can photos, and the panorama mode of the new iPhone 5 is pretty fantastic, so you may find yourself with many more photos than you originally imagined. My wife is a very light iPhone user in terms of apps, but she has lots of sermons, some music and photos of my daughter's wedding. We are constantly managing her space.

In contrast, I am a crazy man, I have heaps of apps, including navigation apps (very large), lots of music and podcasts, and a significant Accordance library, and with my 32GB iphone I am in no problem whatsoever.

If you are just asking is it possible...Darin's answer is spot on. If you are asking for a users perspective...well, now you have one!

I got a 16g and have no problems at all. It boils down to how you use the phone. I am a minimalist with little music, just the apps I use regularly, and only the accordance modules that I need. In other words, I don't have all my music, all apps I ever brought, and all my accordance modules.

If you think you might want a majority of your music, apps, and accordance then go with the highest you can afford. I originally thought 32g but have been fine with 16g. Another consideration is hi-res apps that you use. The more hi-res the more app space you need.

My first iPhone was a 3GS 16g. Like Ken and his wife, I was constantly managing the space. When I upgraded a year ago to a 4S, I went with a 32g. I keep our entire classical music collection on there, rotate sermons on and off as I listen to them, have some pictures, some video (that is also rotated), and just some of my Accordance collection. I find the small screen limits what I do with it. On my iPad, however, I have a large portion of my Accordance library, only a little music, more video (for walking the treadmill). It is also 32g. My husband also has two 32g devices - lots of pictures - he's a great photographer.

The iPhone takes such good pictures that you may find you use it more than you would expect.